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A125759
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Number of n-indecomposable polyominoes.
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7
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OFFSET
| 1,2
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COMMENTS
| A polyomino is called n-indecomposable if it cannot be partitioned (along cell boundaries) into two or more polyominoes each with at least n cells.
MacKinnon incorrectly implies that the sequence is 1,6,44.
MacKinnon only allows polyominoes with >= n cells, leading to A125709 and A125753.
The polyominoes with < 2n cells are uninteresting, leading to A126742 and A126743.
Comment from Peter Pleasants, Feb 18 2007: There is a sense in which n-decomposable polyominoes with >3n-2 cells are also uninteresting: they are precisely the "n-spiders", where an n-spider is a polyomino with a cell whose removal splits it into 4 components each with <n cells.
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REFERENCES
| N. MacKinnon, Some thoughts on polyomino tilings, Math. Gaz., 74 (1990), 31-33.
S. Rinaldi and D. G. Rogers, Indecomposability: polyominoes and polyomino tilings, Math. Gaz., to appear, 2008.
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LINKS
| David Applegate, Pictures of all 2-indecomposable polyominoes
David Applegate, Pictures of all 3-indecomposable polyominoes
David Applegate, Pictures of all 4-indecomposable polyominoes
David Applegate, Pictures of all 5-indecomposable polyominoes
David Applegate, Pictures of all 6-indecomposable polyominoes (gzipped)
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FORMULA
| a(n) = A125709(n) + Sum_{i=1..n-1} A000105(i).
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EXAMPLE
| The six 2-indecomposable polyominoes:
......................X.
X..XX..XXX..XX..XXX..XXX
.............X...X....X.
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CROSSREFS
| Row sums of A125761. Cf. A125709, A125753, A126742, A126743, A000105.
Sequence in context: A184185 A197436 A108432 * A062819 A092336 A161323
Adjacent sequences: A125756 A125757 A125758 * A125760 A125761 A125762
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KEYWORD
| nonn,more
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AUTHOR
| David Applegate (david(AT)research.att.com) and N. J. A. Sloane (njas(AT)research.att.com), Feb 05 2007
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EXTENSIONS
| a(4) and a(5) from Peter Pleasants, Feb 13 2007
a(6) and a(7) from David Applegate (david(AT)research.att.com), Feb 16 2007
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